| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Physics-Informed PDE Solving | 2D Helmholtz (test) | Time (sec/iter)0.0228 | 14 | |
| Inverse PDE solving | Helmholtz full observations | Relative Error0.049 | 14 | |
| Spatio-temporal PDE reconstruction | Helmholtz | PDE Residual0.55 | 12 | |
| PDE Reconstruction | Helmholtz 3% uniformly random measurements | Coefficient Relative L2 Error7.67 | 10 | |
| Forward PDE solving | Helmholtz Full Observation | L2 Relative Error0.0108 | 9 | |
| Forward PDE Solving | Helmholtz (test) | Relative H1 Error0.233 | 9 | |
| Inverse problem | Helmholtz | PDE Residual0.2 | 9 | |
| Forward PDE solving | Helmholtz | PDE Residual0.37 | 9 | |
| PDE Inverse Problem | Helmholtz Noisy | L2 Relative Error67.93 | 7 | |
| PDE Forward Problem | Helmholtz Noisy | L2 Relative Error16.84 | 7 | |
| Conditional source inference | Helmholtz 256 samples (test) | Relative L2 Error0.381 | 6 | |
| Operator Learning for PDEs | Helmholtz (downstream) | EG Score78.3 | 6 | |
| Inverse | Helmholtz 30% noise corruption 1.0 (test) | L2 Relative Error0.5443 | 5 | |
| Forward | Helmholtz 30% noise corruption 1.0 (test) | L2 Relative Error9.16 | 5 | |
| Inverse PDE Solving | Helmholtz 10% noise corruption | L2 Relative Error43.56 | 5 | |
| Forward PDE Solving | Helmholtz 10% noise corruption | L2 Relative Error8.05 | 5 | |
| Inverse | Helmholtz 50% pixels noise | L2 Relative Error0.5999 | 5 | |
| Forward | Helmholtz 50% pixels noise | L2 Relative Error12.04 | 5 | |
| Inverse | Helmholtz 90% pixels corrupted by noise | L2 Relative Error66.93 | 5 | |
| Forward | Helmholtz 90% pixels corrupted by noise | L2 Relative Error16.16 | 5 | |
| Inverse Problem | Helmholtz (test) | RE1.64 | 5 | |
| Forward Problem | Helmholtz (test) | RE2.46 | 5 | |
| Inverse PDE solving | Helmholtz | Relative Error22.6 | 5 | |
| Forward PDE solving | Helmholtz full observations | Relative Error0.023 | 5 | |
| PDE Solving | Helmholtz (test) | Relative L2 Error0 | 3 |